Modeling and Optimization: Theory and Applications [electronic resource] : Selected Contributions from the MOPTA 2010 Conference /
MOPTA 2010(2010 :Lehigh University)
Terlaky, Tamás.editor.
Curtis, Frank E.editor.
This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 18-20, 2010. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Description based upon print version of record.
Modeling and Optimization:Theory and Applications; Preface; Contents; Chapter 1: Obtaining Tighter Relaxations of Mathematical Programs with Complementarity Constraints; 1.1 Introduction; 1.2 Problem Generation and Computational Setup; 1.3 Linear Constraints Based on Bounds on the Variables; 1.3.1 Construction of the Constraints; 1.3.2 Computational Results; 1.4 Linear Constraints Based on Disjunctive Programming; 1.4.1 Disjunctive Cuts; 1.4.2 Computational Results; 1.5 Convex Quadratic Constraints; 1.5.1 Construction of the Constraints; 1.5.2 Computational Results; 1.6 Lifting Constraints
1.7 Semidefinite Constraints1.8 Conclusions; References; Chapter 2: Distributed Optimization in Networking: Recent Advances in Combinatorial and Robust Formulations; 2.1 Introduction; 2.1.1 Garg-Konemann Framework for Fractional Packing Linear Programming Problems; 2.1.2 Markov Approximation for Combinatorial Optimization; 2.1.3 Distributed Robust Optimization; 2.2 P2P Streaming Capacity; 2.2.1 Problem Settings; 2.2.2 Formulation; 2.2.2.1 Single-Session (Primal) Problem; 2.2.2.2 Single-Session Dual Problem; 2.2.3 Algorithm and Performance; 2.2.4 Computing SPT
2.3 Markov Approximation for Combinatorial Optimization2.3.1 General Framework; 2.3.1.1 Problem Formulation; 2.3.1.2 Log-Sum-Exp Approximation; 2.3.1.3 Distributed Markov Chain Monte Carlo; 2.3.2 Application to Distributed P2P Streaming; 2.3.2.1 Settings and Notations; 2.3.2.2 Problem Formulation and Our Approach; 2.3.2.3 Impact of Inaccurate Observations; 2.4 Distributed Robust Optimization; 2.4.1 General Framework; 2.4.1.1 Polyhedron Uncertain Set; 2.4.1.2 D-Norm Uncertainty Set; 2.4.1.3 Ellipsoid Uncertainty Set; 2.4.2 Robust Multipath Rate Control for Network Service Reliability
2.4.2.1 Nominal and Robust Formulations2.4.2.2 Distributed Primal-Dual Algorithms; 2.5 Summary; References; Chapter 3: Fast First-Order Algorithms for Packing-Covering Semidefinite Programs; 3.1 Introduction; 3.1.1 Preliminaries; 3.2 The Packing-Covering SDP; 3.3 Approximating the Packing-Covering SDP; 3.3.1 Approximating the Relaxed Packing-Covering SDP; 3.3.2 Bisection Search; 3.4 Applications; 3.4.1 Vertex Cover; 3.4.2 Min Uncut; 3.4.3 Scheduling; References; Chapter 4: On the Tendency Toward Convexity of the Vector Sum of Sets; References
Chapter 5: Multiobjective Optimization via Parametric Optimization: Models, Algorithms, and Applications5.1 Introduction; 5.2 Multiobjective and Parametric Optimization; 5.2.1 Weighting Method; 5.2.2 -Constrained Method; 5.2.3 Parametric Optimization; 5.2.4 Multiobjective Optimization via Parametric Optimization; 5.2.5 Multiobjective and Parametric Quadratic Optimization; 5.3 Solving Parametric Optimization Problems; 5.3.1 Uni-Parametric Linear and Convex Quadratic Optimization; 5.3.2 From Uni- to Bi-Parametric Optimization; 5.3.2.1 Detecting the Boundary of an Invariancy Region
5.3.2.2 Transition from an Invariancy Region to the Adjacent Invariancy Regions
Includes bibliographical references.
This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 18-20, 2010. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Mathematical models.
Mathematical optimization.
Applied mathematics.
Engineering mathematics.
Mathematical Modeling and Industrial Mathematics.
Optimization.
Mathematical and Computational Engineering.